How disclosure quality affects the level of information asymmetry

Abstract

We examine two potential mechanisms through which disclosure quality is expected to reduce information asymmetry: (1) altering the trading incentives of informed and uninformed investors so that there is relatively less trading by privately informed investors, and (2) reducing the likelihood that investors discover and trade on private information. Our results indicate that the negative relation between disclosure quality and information asymmetry is primarily caused by the latter mechanism. While information asymmetry is negatively associated with the quality of the annual report and investor relations activities, it is positively associated with quarterly report disclosure quality. Additionally, we hypothesize and find that that the negative association between disclosure quality and information asymmetry is stronger in settings characterized by higher levels of firm-investor asymmetry.

Appendix: Venter and de Jongh (2004) Extension of EKO model

The extended EKO model allows for the daily level of trading intensity to vary with a daily trading intensity factor, W _t . The distribution of buys (B) and sells (S) on day t is given by

• (B _t , S _t ) | no-news, W _t ∼ Independent Bivariate Poisson (ɛW _t , ɛW _t )

• (B _t , S _t ) | bad-news, W _t ∼ Independent Bivariate Poisson (ɛW _t , ɛ(1 + ν)W _t )

• (B _t , S _t ) | good-news, W _t ∼ Independent Bivariate Poisson (ɛ(1 + ν)W _t , ɛW _t ).

The likelihood function induced by the model for a trading day, conditional on the Poisson trading intensities λ _Bt and λ _St for buys and sells, respectively, is given by:

$$ L_t(B_t ,S_t \vert \lambda_{Bt},\lambda_{St})=f_{POISS}(B_t,S_t\vert \lambda _{Bt},\lambda _{St})=\frac{(\lambda _{Bt})^{B_t}}{B_t!}\ast \frac{(\lambda_{St})^{S_t}}{S_t !}\ast e^{-\lambda_{Bt}-\lambda _{St}}. $$

(A1)

The overall likelihood function is a “mixture” model where the weights on the three components (no news, bad news, and good news) reflect the probabilities of their occurrence in the data. Denote the trading intensity associated with a no-news day (uninformed traders only) by ${\lambda_{Nt}=\varepsilon W_{t}}$ and the joint informed and uninformed trading intensity by ${\lambda_{It}= \varepsilon(1+\nu)W_{t}}$. Thus:

$$ \begin{aligned} \;&L_t(B_t ,S_t \vert \lambda_{Nt},\lambda _{It} )=L_t (B_t,S_t\vert \varepsilon ,\mu ,W_t)\\ &= (1-\alpha )f_{POISS} (B_t ,S_t \vert \lambda _{Nt} ,\lambda _{Nt} )+\alpha \delta f_{POISS} (B_t ,S_t \vert \lambda _{Nt} ,\lambda _{It} )+\alpha (1-\delta )f_{POISS} (B_t ,S_t \vert \lambda _{It} ,\lambda_{Nt})\\ &=(1-\alpha)\frac{\lambda _{Nt}^{^{B_t}}}{B_t!}\ast \frac{\lambda _{Nt}^{^{S_t}}}{S_t !}\ast e^{(-2\lambda _{Nt})}+\alpha \delta \frac{\lambda _{Nt}^{^{B_t }}}{B_t !}\ast \frac{\lambda _{It}^{^{S_t}} }{S_t!}\ast e^{(-\lambda _{Nt}-\lambda _{It})}+\alpha (1-\delta )\frac{\lambda _{It}^{^{B_t }}}{B_t !}\ast \frac{\lambda _{Nt}^{^{S_t}} }{S_t!}\ast e^{(-\lambda _{It}-\lambda _{Nt})}. \end{aligned} $$

(A2)

The random variable W is assumed to have a unit inverse Gaussian distribution with parameter ψ > 0. The density function of W is given by

$$ f_{UIG} (w;\psi )=\frac{\psi \hbox{exp}(\psi^2)}{\sqrt{2\pi} }w^{-\frac{3}{2}}\hbox{exp}\left(-\frac{1}{2}\psi^2(w^{-1}+w)\right),\quad w > 0. $$

(A3)

The expected value of this distribution is equal to one and the variance is equal to (1/ψ²). Thus, as ψ→∞, the variance in daily trading intensities induced by general market conditions goes to zero and the extended model reduces to the basic EKO model.

The distributional assumption for W implies that the joint distribution of B _t and S _t is given by a multivariate Poisson inverse Gaussian distribution (Stein, Zucchini, & Juritz, 1987). If λ₁ (λ₂) is the base level of trading intensity for buys (sells) on a particular day (i.e., λ _Bt  = W _t λ₁ and λ _St  = W _t λ₂), then the likelihood function for observing the mixed Poisson distribution of B _t buys and S _t sells is:

$$ \begin{aligned} f_{PIG} =f_{PIG}(B_t ,S_t \vert \lambda_1,\lambda _2 ,\psi)=\\ \frac{(\lambda_{1})^{B_{t}}}{B_{t}!}*\frac{(\lambda_{2})^{S_{t}}} {S_{t}!}*{\left[{\frac{\psi^{2}}{{\psi^{2}+2{\left({\lambda_{1}+ \lambda_{2}}\right)}}}}\right]}^{{\frac{B_{t}+S_{t}}{2}}}{*e}(\psi^{2}- \psi\sqrt{(\psi^{2}+2(\lambda_{1}+\lambda_{2}))} *\hat{{\mathbf K}} _{\left(B_{t}+S_{t}-\frac{1}{2}\right)}\left(\psi\sqrt{(\psi^{2}+2(\lambda_{1}+\lambda_{2}))}\right) \end{aligned} $$

(A4)

where ${\mathop{\mathbf K}\limits^\wedge{}_{n}(z)={K_n (z)}\mathord{\left/ {\vphantom {{K_n(z)}{K_{0.5} (z)}}}\right. K_{0.5}(z)}}$ and K _n (z) is the modified Bessel function of the second kind. Then, the expectation of B _t is given by ${\hbox{E}[B_{t}]=\hbox{E}[B_{t}\vert W_{t}]=\hbox{E}[\lambda_{1} W_{t}]=\lambda_{1}}$ and ${\hbox{Var}(B_{t})=\lambda_{1} +(\lambda _{1}/\psi^{2});}$ similarly for S _t . The covariance of B _t and S _t is given by ${\hbox{Cov}(B_{t},S_{t})=(\lambda_{1}\lambda_{2})/\psi^{2}}$. Therefore, the expected values of B _t and S _t are given by λ₁ and λ₂—as in the basic EKO model. However, in the extended model, if ${\psi\ne\infty}$, then the dispersions of B _t and S _t are higher than those in the EKO model and the daily values of buys and sells are positively correlated. Therefore, the full likelihood function is given by

$$ \begin{aligned} &L_t (B_t ,S_t \vert \alpha ,\delta ,\psi ,\varepsilon ,\nu )=\\ &(1-\alpha )f_{PIG} (B_t ,S_t \vert \varepsilon ,\varepsilon ,\psi)+\alpha \delta f_{PIG} (B_t ,S_t \vert \varepsilon ,\varepsilon (1+\nu),\psi )+\alpha (1-\delta )f_{PIG} (B_t ,S_t \vert \varepsilon (1+\nu),\varepsilon ,\psi ). \end{aligned} $$

(A5)